Electron. J. Differential Equations,
Vol. 2017 (2017), No. 170, pp. 112.
Solvability of a nonlocal problem for a hyperbolic
equation with integral conditions
Anar T. Assanova
Abstract:
We study a nonlocal problem with integral conditions for a hyperbolic equation
two independent variables. By introducing additional functional parameters,
we investigated the solvability and construction of approximate solutions.
The original problem is reduced to an equivalent problem consisting of
the Goursat problems for a hyperbolic equation with parameters and the
boundary value problem with integral condition for the ordinary differential
equations with respect to the parameters. Based on the algorithms for finding
solutions to the equivalent problem, we propose algorithms for finding
the approximate solutions, and prove their convergence.
Coefficient criteria for the unique solvability of nonlocal problem with
integral conditions for hyperbolic equation with mixed derivative are
also established.
Submitted March 17, 2017. Published July 6, 2017.
Math Subject Classifications: 35L51, 35L53, 35R30, 34B10.
Key Words: Hyperbolic equation; nonlocal problem; integral condition; algorithm;
approximate solution.
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Anar T. Assanova
Department of Differential Equations
Institute of Mathematics and Mathematical Modeling
125, Pushkin str., 050010 Almaty, Kazakhstan
email: assanova@math.kz, anarasanova@list.ru

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